Problem: Rewrite as a simplified fraction. ${0.16\overline{1} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 161.1111...\\ 100x &= 16.1111...\end{align*}}$ Subtracting the two equations, we have: ${900x = 145}$ ${x = \dfrac{145}{900}} $ ${x = \dfrac{29}{180}} $